Open-Ended Mathematics Tasks: How Did a Middle School Teacher Interpret and Use Information Acquired through the Examination of Student Responses?

Moskal, Barbara

A pilot study was conducted to examine the information with respect to the modes, referents, and relationships that a given teacher acquires through the examination of her students' written responses to open-ended tasks and how the teacher uses this information. The participating teacher taught sixth grade in a public elementary school in a suburban neighborhood. The teacher had been trained in the rating of open-ended tasks according to pre-established criteria as part of a larger project. Tasks requiring computing areas and averaging were administered to students. The teacher was asked to predict how students would perform on each task and to suggest the approaches they would use. The teacher was later interviewed as she examined students' responses to the tasks to complete a Task Knowledge Inventory. The analysis of the teacher's responses suggests that she did have an adequate understanding of the concepts that were assessed in each task. She was aware that the students would use different approaches. The students' responses did offer the teacher information she did not previously possess. She was not able to predict accurately the methods the students would use to solve these problems, and she gained information about the depth of their knowledge and the referents they used in problem solving. The bulk of the teacher's attention during the students' acquisition process was on the individual, but her discussion of potential uses was focused on the larger group for instructional decision making. Results suggest that the teacher actually acquired more information about the students through the examination process than she used, especially with regard to students' communication processes. (Contains 6 tables, 8 figures, and 30 references.) (SLD)